More than 380 Pg of carbon have been released by human activities from fossil fuel combustion and cement manufacturing since the beginning of the Industrial Revolution. This carbon release has caused atmospheric CO2 levels to increase by ~100 ppmv compared to the highest interglacial value of the last ~800,000 years. Net uptake of carbon by the oceans has caused the surface ocean pH to drop by ~0.1 pH units. Evaluating carbon sequestration options is now timely. We use the carbon-cycle model LOSCAR to evaluate the effects of artificially enhancing ocean alkalinity from year 2020 to year 2400 on ocean pH and atmospheric pCO2. Ten different carbon emission scenarios with scaled alkalinity input are simulated. Results show that for ocean pH to be maintained above 8.0, on the order of 2–10 × 1014 moles of alkalinity/year for C emissions of 1500–5000 Pg C, respectively, is required. Atmospheric pCO2 remains high (500–600 ppmv) in nine of the carbon emission scenarios. Ocean alkalization, if ever implemented at such a large scale, could allow ocean pH to be stabilized but pCO2 would not return to pre-industrial levels. Cost estimates of the ocean alkalization operation, using quicklime (CaO) was estimated to range from 0.5 to 2.8 $US trillion/year, depending on the target pH selected to avoid damage to marine organisms and ecosystems. For comparison, this cost is ~0.8% and ~4.6% of the 2011 global Gross Domestic Product for total anthropogenic carbon emissions of 1500 and 5000 Pg C, respectively. The cost of 1 ton of CO2 sequestered ranges from 103 to 144 $US for total emissions of 1500–5000 Pg C, respectively. Producing large amounts of quicklime (without carbon capture and storage) would cause substantial additional CO2 release. This reduces the fossil fuel emissions allowed to maintain pH above 8.0 by a factor of 1.3–2.5 (for total emissions of 1000 and 5000 Pg C, respectively).